Let us also recall that starting from a moduli space \(\mathcal {M}\)  of Higgs bundles, the nonabelian Hodge correspondence and Riemann–Hilbert map associate to \(\mathcal {M}\)  two other moduli spaces, of local systems and of monodromy data (known as de Rahm and Betti models, see [1]} for a nice overview). For our case, these two other incarnations can be found in [2]}, [3]}, see also [4]}, [5]}, [6]}, [7]}, [8]} for further links between the Inozemtsev system and isomonodromic deformations.
